Squeeze each tomato thoroughly to ensure most seeds are removed. Set the tomatoes aside.
Cut carrot, onion, and celery into uniform sizes and combine with olive oil and garlic in a non-reactive roasting pan over low heat. Sweat the mirepoix until the carrots are tender and the onion becomes translucent, 15 to 20 minutes. Add the tomatoes and capers to the roasting pan.
Place roasting pan on the middle rack of the oven and broil for 15 to 20 minutes, stirring every 5 minutes. Tomatoes should start to brown slightly on edges with light caramelization. Remove the pan from the broiler. Place the pan over 2 burners on the stove. Add the white wine to the tomatoes and cook for 2 to 3 more minutes over medium heat.